Exponential stabilization of a class of unstable bilinear systems

Considers the control design of bilinear systems with multiplicative control inputs. Previous control designs for such systems normally assume that the open-loop bilinear system is (neutrally) stable. In this paper, a nonlinear control design is proposed for open-loop unstable bilinear systems. The new control stabilizes the bilinear system globally and exponentially if a sufficient stability condition, which can be checked by off-line computer simulations in advance of the control, is satisfied